Understanding Key Financial Ratios in Modern Portfolio Theory
Investing is about balancing risk and return. But how do we quantify these? How can we compare one investment’s performance to another, particularly when they involve different levels of risk? This is where financial ratios—grounded in Modern Portfolio Theory (MPT)—become essential.
These are all statistical measurements used to evaluate an investment's risk-return profile. Each plays a distinct role in helping investors make more informed decisions.
Risk Measures
Risk in investing can be broadly defined in two ways:
Volatility of returns, captured by standard deviation
Systematic or market risk, captured by beta
Standard Deviation
Standard deviation measures how much an investment’s returns deviate from its mean average over time. The higher the standard deviation, the greater the volatility and, consequently, the greater the uncertainty around future returns. Whilst volatility is not inherently negative, it represents unpredictability that investors must consider.
Beta
Beta quantifies an investment’s sensitivity to movements in the broader market. A beta of 1 indicates that the investment tends to move in line with the market. A beta greater than 1 suggests more volatility than the market, whereas a beta below 1 indicates lower volatility.
For example, if a stock has a beta of 1.2 and the market rises by 10%, the stock would be expected to rise by around 12%, and fall similarly if the market declines.
Risk-Adjusted Return Measures
Headline returns do not tell the full story. Investors also need to consider how much risk was taken to achieve those returns. Three core metrics help assess risk-adjusted performance:
Sharpe ratio
Alpha
Information ratio
Sharpe Ratio
The Sharpe ratio, developed by William F. Sharpe, compares the excess return of an investment over the risk-free rate to the total volatility of those returns:
Sharpe Ratio = (Rp – Rf) / σp
Where:
Rp = Portfolio return
Rf = Risk-free rate
σp = Standard deviation of portfolio returns
A higher Sharpe ratio indicates that the investor is being better compensated for each unit of risk taken. It rewards consistency and penalises excessive volatility, treating upside and downside deviation equally.
Risk, in this context, is measured by volatility—how much the return of an investment goes up and down over time. That volatility is quantified using standard deviation.
So, when we say:
‘The Sharpe ratio tells you how much return you receive per unit of risk taken,’
We mean:
How much excess return you earn for each 1% of volatility (standard deviation) you’re exposed to.
For example:
Investment A has an excess return of 10%, and volatility (risk) of 5%.
Sharpe ratio = 10 / 5 = 2
That means for every 1% of risk taken, you’re earning 2% in return—which is quite efficient.
The size difference in Sharpe ratios matters, especially when comparing investments or portfolios. Here’s a general rule of thumb:
A difference of 0.1–0.2 might be noticeable, but not huge—it could still fall within statistical noise depending on sample size.
A difference of 0.3–0.5 is usually meaningful—it often reflects a material difference in risk-adjusted performance.
A difference > 0.5 is typically significant—suggesting that one investment is much more efficient at delivering return for the level of risk taken.
Alpha
Alpha measures the excess return of an investment relative to the return predicted by its level of systematic risk (beta), according to the Capital Asset Pricing Model (CAPM):
Alpha (α) = Rp – [Rf + βp(Rm – Rf)]
Where:
Rp = Portfolio return
Rf = Risk-free rate
βp = Portfolio beta
Rm = Market return
Alpha is therefore the return above (or below) what would be expected given the portfolio’s exposure to market risk. A positive alpha indicates outperformance; a negative alpha suggests underperformance.
Information Ratio
The information ratio builds on alpha by measuring it relative to the tracking error, which is the standard deviation of the portfolio’s excess return over the benchmark:
Information Ratio = (Rp – Rb) / TE
Where:
Rp = Portfolio return
Rb = Benchmark return
TE = Tracking error
This ratio reflects both the magnitude and the consistency of active returns. It is particularly useful for assessing the skill of active managers whose goal is to outperform a specific benchmark.
Additional Metrics
Sortino Ratio
The Sortino ratio refines the Sharpe ratio by focusing only on downside volatility—recognising that investors are more concerned about losses than gains. It replaces the standard deviation with downside deviation, which considers only negative returns relative to a minimum acceptable return:
Sortino Ratio = (Rp – Rf) / σd
Where:
Rp = Portfolio return
Rf = Risk-free rate
σd = Downside deviation
This makes the Sortino ratio particularly relevant for portfolios aimed at capital preservation or retirement income.
R-Squared
R-squared measures how well a portfolio’s returns are explained by movements in a benchmark. It ranges from 0% to 100%.
A high R-squared (typically above 85%) means that the benchmark is a good explanatory model for the portfolio.
A low R-squared suggests that the portfolio behaves more independently.
Whilst R-squared does not measure performance, it does help assess the reliability of other metrics such as beta and alpha. If R-squared is low, these measures may have limited explanatory value.
Final Thoughts
Each of these financial ratios offers a different lens through which to assess investment performance. Together, they form a powerful framework for understanding not only how much return an investment has generated, but whether that return was earned efficiently given the risk taken.
No single measure tells the whole story. These ratios—whilst statistically robust—are sensitive to timeframes, benchmark selection, and assumptions. They are best used together, with a clear understanding of what each one reveals.
As Modern Portfolio Theory reminds us, the goal is not to eliminate risk, but to be fairly compensated for bearing it.